The rapid development of superconducting quantum electronics has motivated a search for quantum-limited amplifiers for the low-noise readout of qubits and linear cavity resonators. Conventional approaches have relied upon dc Superconducting QUantum Interference Devices (dc SQUID) that can achieve noise performance approaching the fundamental quantum limit imposed on phase-insensitive linear amplifiers—namely, the amplifier adds at least half a quantum of noise to the signal it amplifies.
Although approaches employing SQUID are, in principle, capable of amplifying signals at frequencies approaching the Josephson frequency (typically in the tens of GHz), it remains challenging to embed the SQUID in a traditional transmission line environment. As used herein, a transmission line or transmission line environment refers to a conductor, including a conductive trace in an integrated circuit (IC), that is specifically designed to carry alternating currents with sufficient frequencies for the signal to have properties of a wave. Such transmission line environments typically are a 50 Ohm (Ω) or even 75Ω environment. Accordingly, it is challenging to utilize a traditional SQUID-based amplifier within a transmission line environment because it is difficult to match the inductive coupling input and the output of a SQUID-based amplifier to common transmission line environments. For example, the inductive coupling input of the SQUID-based amplifier presents not only an obvious inductive component but also substantial parasitic reactance. Modeling and accounting for these characteristics of the SQUID-based amplifier can be challenging, particularly, when the input signal is a weak microwave tone employed as a dispersive probe of the quantum state of a superconducting or semiconducting qubit.
For quantum information processing applications related to the low-noise readout of qubits and linear cavity resonators, one requires ultrasensitive amplifiers operating in the radiofrequency (RF) or microwave range. Using traditional amplifier designs, such as SQUID-based designs, it can be challenging to provide for efficient coupling of an RF or microwave signal to the device. For example, the parasitic capacitance of the SQUID-based amplifier substantially impedes the effectiveness of the amplifier architecture when utilized in the RF or microwave range. To combat the losses experienced with SQUID-based amplifiers when used in the RF or microwave range, some have attempted to tune the amplifier input to have a resonance matched to the expected input signal frequency. This strategy, though adding to the overall complexity of the circuit design and modeling capabilities and reducing the flexibility of a given SQUID-based amplifier to be utilized with a varied input frequency range, often fails in the RF and microwave frequency range due to the fact that coupling efficiency decreases significantly with increasing operating frequency.
Case in point, recently, it was shown that near quantum-limited performance can be achieved with a microstrip SQUID-based amplifier, where the input coil of the amplifier is configured as a microstrip resonator with the SQUID washer acting as a groundplane. In this case, the noise temperature of the microstrip SQUID amplifier, when cooled to millikelvin temperatures, was measured to be 47±10 mK and 48±5 mK at frequencies of 519 MHz and 612 MHz, respectively. This performance was more than an order of magnitude lower than the best semiconductor amplifiers available and within a factor of 2 of the quantum limit. However, efforts to extend the operating frequencies of these amplifiers into the gigahertz range are hampered by the fact that reduction of the length of the input resonator is coupled to reduction of the mutual inductance between the input coil and the SQUID. Alternative approaches have included the integration of a high-gain SQUID gradiometer into a coplanar waveguide resonator at a current antinode.
Accordingly, when used in higher-frequency applications, SQUID-based amplifiers tend to have substantially limiting characteristics that impede practical implementations. Specifically, SQUID-based amplifier devices have relatively low gain-bandwidth product in the microwave frequency range.
Thus, it would be desirable to have a system and method for processing and amplifying readout signals having characteristics commonly associated with quantum computing, particularly, when the signals reach frequencies in the RF and microwave range.